Audible noise means it isn't modulating the original signal, so I disagree that it's always inherently bad. Some beloved amplifiers are simply "noisy", and they are revered anyways. If you have modulating noise and audible noise, that matters. In general I'd say if you can't hear it anywhere near the listening position it isn't an issue so long as it isn't a hum.
Hum does mean a loop typically, so I agree there, that is usually affecting the signal. Once again, I say, try disconnecting the PSU and listen (the battery will be charged and last for a long time, then just plug it in between listens).
Will do. Fortunately there is no hum just quiet hiss now inaudible from a foot away and quieter than my Kondom1000 mk 2 and Kaguras.